The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  1  1
 0  X  0  0  0  X  X  X  2  2  0 X+2  X  2 X+2 X+2  2  X  0 X+2  0  2  X  X  0  0 X+2  0 X+2  2  X  2 X+2 X+2  X X+2  X  2  0  2  2  0 X+2 X+2
 0  0  X  0  X  X X+2  0  2  X  2  X  0  X X+2  0  0  2  2 X+2 X+2 X+2 X+2  2  0  X  X  0  2  X  X  2  0  0 X+2  0  2 X+2  X  X  0  2  X X+2
 0  0  0  X  X  0  X X+2  2  X X+2  2  X  0  X  0 X+2  X  0  2  X  2 X+2  2 X+2 X+2  X  2  2  2  2  X X+2  X  2  2  0 X+2 X+2  X  0  X X+2 X+2

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+43x^40+58x^42+128x^43+61x^44+128x^45+52x^46+32x^48+2x^50+6x^52+1x^84

The gray image is a code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 0.039 seconds.